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Finite Element Convergence for Time-Dependent PDEs with a Point Source in COMSOL 4

M. Gobbert, and D. Trott University of Maryland Baltimore County
Baltimore, MD

Many application problems have non-smooth forcing terms, such as the Dirac delta function. The convergence order for the FEM solution is limited by the regularity of the solution in this case.

This paper presents information on the techniques needed in COMSOL 4 to enable FEM convergence studies for time-dependent problems of this type, including how to correctly implement the Dirac delta function for a time-dependent problem, how to set up a study with repeated uniform mesh refinement at several points in time, and how to use a reference solution since no analytic PDE solution is available.